Question

A recent study of newborns used umbilical cord blood to test for 25 hydroxyvitamin D, which is an indicator of vitamin D status of the baby. It was reported that 65% of babies tested were deficient in vitamin D in spite of the fact that the mother consumed vitamin D supplements during pregnancy. A researcher in a northern region felt that this percentage should be lower for this region because with reduced hours of sunshine during winter months, pregnant women tended to use of higher doses of supplements to compensate. A sample of 125 newborns was tested, and 72 were declared to be deficient in vitamin c.

1. State the appropriate null and alternative hypotheses, in symbols

2. Calculate the test statistic

3. Calculate the p-value

4. Would you reject the null hypothesis at the @=.05 significance level? Explain

5. Write one sentence conclusion summarizing what the data reveals.

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis: p = 0.65
Alternative Hypothesis: p < 0.65

2)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.576 - 0.65)/sqrt(0.65*(1-0.65)/125)
z = -1.73

3)

P-value Approach
P-value = 0.0414

5)

As P-value < 0.05, reject the null hypothesis.

6)

There is sufficient evidence to conclude that he mother consumed vitamin D supplements during pregnancy. A researcher in a northern region felt that this percentage should be lower for this region because with reduced hours of sunshine during winter months, pregnant women tended to use of higher doses of supplements to compensate